Finite Group Databasebeta

← #13079686

Subgroups — #13079686

Order 1408.

396 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623361C211yesmaximal, characteristic
2#10623156C211yesmaximal, characteristic, complemented
3C11×#452C211yesmaximal, characteristic, complemented
4#10622852C211yesmaximal, characteristic, complemented
5#10622803C211yesmaximal, characteristic, complemented
6#10622798C211yesmaximal, characteristic, complemented
7#10622788C211yesmaximal, characteristic, complemented
8#10622776C211yesmaximal, characteristic, complemented
9#10622659C211yesmaximal, characteristic, complemented
10#10622413C211yesmaximal, characteristic, complemented
11#10622411C211yesmaximal, characteristic, complemented
12#10622377C211yesmaximal, characteristic, complemented
13#10622375C211yesmaximal, characteristic, complemented
14#10622344C211yesmaximal, characteristic, complemented
15#10622333C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C22×D44C2211yescharacteristic
18C2×C11×Q16C2211yescharacteristic, complemented
19C2×C11×SD16C2211yescharacteristic, complemented
20C11×C22⋊Q8C2211yescharacteristic
21#67000C2211yescharacteristic
22#67000C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic, complemented
24#66997C2211yescharacteristic, complemented
25C2×#4326C2211yescharacteristic, complemented
26C2×#4325C2211yescharacteristic
27C2×#4325C2211yescharacteristic
28#66993C2211yescharacteristic
29#66993C2211yescharacteristic
30#66990—21no—
31#66990—21no—
32C2×#4324C2211yescharacteristic, complemented
33#66983—21no—
34#66983—21no—
35#66979C2211yescharacteristic
36#66977C2211yescharacteristic
37C2×#4314C2211yescharacteristic
38C2×#4314C2211yescharacteristic
39#66943—21no—
40#66943C2211yescharacteristic, complemented
41#66942—21no—
42#66940C2211yescharacteristic, complemented
43#66932—21no—
44#66932—21no—
45C11×#103C2211yescharacteristic, complemented
46C11×#102C2211yescharacteristic, complemented
47C11×C22⋊C8C2211yescharacteristic
48#66899C2211yescharacteristic, complemented
49#66896C2211yescharacteristic, complemented
50C22⋊(C11⋊C8)C2211yescharacteristic
51#66885C2211yescharacteristic
52#66885C2211yescharacteristic
53#66879C2211yescharacteristic, complemented
54Dic11⋊C8C2211yescharacteristic, complemented
55Dic11⋊C8C2211yescharacteristic, complemented
56C8×Dic11C2211yescharacteristic, complemented
57#66873C2211yescharacteristic
58#66873C2211yescharacteristic
59C23×D11—21no—
60C11×#41—41no—
61C11×#41—41no—
62C2×Q8×C11C2311yescharacteristic
63C2×Q8×C11C2311yescharacteristic
64C2×D4×C11—21no—
65C2×D4×C11C2311yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11C2311yescharacteristic
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C2×C22⋊D11—21no—
72C2×D44—21no—
73C2×D44—41no—
74C2×D44—41no—
75C2×D44C2311yescharacteristic
76C2×D44C2311yescharacteristic
77C2×Dic22C2311yescharacteristic
78C11×Q16—41no—
79C11×SD16—41no—
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C11×C4⋊C4—21no—
83C11×C4⋊C4C2311yescharacteristic
84C11×C22⋊C4—21no—
85C22⋊Dic11—21no—
86C22⋊Dic11D411yescharacteristic
87C22⋊Dic11D411yescharacteristic
88#4326—41no—
89#4325—41no—
90#4325—41no—
91#4324—41no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11D411yescharacteristic
99C4⋊Dic11D411yescharacteristic
100C4⋊Dic11C2311yescharacteristic
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108C4×Dic11C2311yescharacteristic
109C4×Dic11C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112#4314—41no—
113#4314—41no—
114#3222—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11C2×D411yescharacteristic
117C22×D11—21no—
118C22×D11—21no—
119C22×D11—42no—
120C22×D11—81no—
121C22×D11—81no—
122Q8×C11—21no—
123Q8×C11—21no—
124Q8×C11—21no—
125Q8×C11—21no—
126D4×C11—21no—
127D4×C11—21no—
128D4×C11—42no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—42no—
135C2×C4×C11C2×D411yescharacteristic
136C2×C4×C11C2411yescharacteristic
137C22⋊D11—81no—
138C22⋊D11—81no—
139C22⋊D11—81no—
140C22⋊D11—81no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11C2×D411yescharacteristic
144C2×Dic11C2×D411yescharacteristic
145C2×Dic11C2×D411yescharacteristic
146C2×Dic11C2×D411yescharacteristic
147D44—21no—
148D44—21no—
149D44—21no—
150D44—21no—
151D44—42no—
152Dic22—21no—
153Dic22—21no—
154C8×C11—21no—
155C8×C11—21no—
156C11⋊C8—21no—
157C11⋊C8—21no—
158#541—111no—
159#535—111no—
160#497—111no—
161#492—111no—
162#490—111no—
163#488—111no—
164#464—111no—
165#464—111no—
166#460—111no—
167#460—111no—
168#452—111no—
169#452D1111yescharacteristic, complemented
170#450—111no—
171#450—111no—
172#433—111no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11C22×D411yescharacteristic
180C2×D11—41no—
181C2×D11—41no—
182C2×D11—41no—
183C2×D11—41no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—84no—
187C4×C11—21no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11H(5,𝔽2)11yescharacteristic
192C4×C11H(5,𝔽2)11yescharacteristic
193Dic11—21no—
194Dic11—21no—
195Dic11—21no—
196Dic11—21no—
197Dic11—41no—
198Dic11—41no—
199C2×#41C2×D1111yescharacteristic
200C22×D4—111no—
201C2×Q16—111no—
202C2×Q16C2×D1111yescharacteristic, complemented
203C2×SD16—111no—
204C2×SD16—111no—
205C2×SD16—111no—
206C2×SD16—111no—
207C2×SD16—111no—
208C2×SD16C2×D1111yescharacteristic, complemented
209C4⋊Q8—111no—
210#127—111no—
211#127—111no—
212#126—221no—
213#126—221no—
214#125—111no—
215#125—221no—
216#125—221no—
217#124—111no—
218#124—111no—
219C22⋊Q8—111no—
220C22⋊Q8C2×D1111yescharacteristic
221#121—221no—
222#121—221no—
223#120—221no—
224#120—221no—
225C4×Q8—111no—
226C4×Q8—111no—
227#117—111no—
228C4⋊C8—111no—
229C4⋊C8—111no—
230#103—111no—
231#103C2×D1111yescharacteristic, complemented
232#102—111no—
233#102—111no—
234#102—111no—
235#102—111no—
236#102—111no—
237#102C2×D1111yescharacteristic, complemented
238C22⋊C8—111no—
239C22⋊C8C2×D1111yescharacteristic
240#97—111no—
241C4×C8—111no—
242C2×C11—41no—
243C2×C11—81no—
244C2×C11#53511yescharacteristic
245C2×C11#57711yescharacteristic
246C2×C11#57711yescharacteristic
247D11—81no—
248D11—81no—
249C24—221no—
250#41—41no—
251#41—41no—
252C2×Q8—111no—
253C2×Q8C22×D1111yescharacteristic
254C2×Q8C22×D1111yescharacteristic
255C2×D4—21no—
256C2×D4—111no—
257C2×D4—111no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—221no—
262C2×D4—221no—
263C2×D4—441no—
264C2×D4—441no—
265C2×D4C22×D1111yescharacteristic
266C22×C4—21no—
267C22×C4C22×D1111yescharacteristic
268Q16—41no—
269Q16—441no—
270SD16—41no—
271SD16—441no—
272SD16—441no—
273SD16—441no—
274SD16—441no—
275SD16—441no—
276C2×C8—111no—
277C2×C8—111no—
278C2×C8C22×D1111yescharacteristic
279C2×C8C22×D1111yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—111no—
282C4⋊C4—111no—
283C4⋊C4—111no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C4⋊C4—221no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4C22×D1111yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—111no—
294C22⋊C4—111no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4—221no—
298C22⋊C4—221no—
299C22⋊C4—221no—
300C42—111no—
301C42—111no—
302C42—221no—
303C42—221no—
304C11#322211yescharacteristic, complemented, Sylow
305C23—21no—
306C23—221no—
307C23—221no—
308C23—442no—
309C23—881no—
310C23—881no—
311C23D4×D1111yescharacteristic
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—21no—
316Q8—221no—
317Q8—221no—
318D4—21no—
319D4—21no—
320D4—42no—
321D4—221no—
322D4—221no—
323D4—221no—
324D4—221no—
325D4—442no—
326D4—881no—
327D4—881no—
328D4—881no—
329D4—881no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—111no—
337C2×C4—111no—
338C2×C4—111no—
339C2×C4—111no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4D4×D1111yescharacteristic
343C2×C4C23×D1111yescharacteristic
344C8—21no—
345C8—21no—
346C8—221no—
347C8—221no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—441no—
355C22—441no—
356C22—441no—
357C22—441no—
358C22—441no—
359C22—441no—
360C22—884no—
361C22C2×D4×D1111yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—221no—
367C4—221no—
368C4—221no—
369C4—221no—
370C4—441no—
371C4—441no—
372C4#6703711yescharacteristic
373C4#6703711yescharacteristic
374C2—41no—
375C2—81no—
376C2—881no—
377C2—881no—
378C2#1062312311yescharacteristic
379C2#1062330111yescharacteristic
380C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#452C2
socleC22×C11C22×D4
prime radical#10623361C2
hypercenter#452D11
hypocenterC11#3222
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10623156C2semidirect
3. C11×#452C2semidirect
4. #10622852C2semidirect
5. #10622803C2semidirect
6. #10622798C2semidirect
7. #10622788C2semidirect
8. #10622776C2semidirect
9. #10622659C2semidirect
10. #10622413C2semidirect
11. #10622411C2semidirect
12. #10622377C2semidirect
13. #10622375C2semidirect
14. #10622344C2semidirect
15. #10622333C2semidirect
18. C2×C11×Q16C22semidirect
19. C2×C11×SD16C22semidirect
23. Q8×Dic11C22semidirect
24. #66997C22semidirect
25. C2×#4326C22semidirect
32. C2×#4324C22semidirect
40. #66943C22semidirect
42. #66940C22semidirect
45. C11×#103C22semidirect
46. C11×#102C22semidirect
48. #66899C22semidirect
49. #66896C22semidirect
53. #66879C22semidirect
54. Dic11⋊C8C22semidirect
55. Dic11⋊C8C22semidirect
56. C8×Dic11C22semidirect
169. #452D11semidirect
202. C2×Q16C2×D11semidirect
208. C2×SD16C2×D11semidirect
231. #103C2×D11semidirect
237. #102C2×D11semidirect
304. C11#3222semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#106233612
#106231562
C11×#4522
#106228522
#106228032
#106227982
#106227882
#106227762
#106226592
#106224132
#106224112
#106223772
#106223752
#106223442
#106223332
#322211